On Some Estimation Methods of Neutrosophic Continuous Probability Distributions Using One-Dimensional AH-Isometry

Abstract

In this research, we introduce an algebraic approach to define the concept of neutrosophic maximum likelihood estimation method based on neutrosophic continuous probability distributions based on classical neutrosophic numbers of the form 𝑁 = 𝑎 + 𝑏𝐼;𝐼 2 = 𝐼 i.e., 𝐼 is a letter not a numerical set. We prove that the neutrosophic loglikelihood function gives the same estimators given by neutrosophic likelihood function. Also, we present the concept of neutrosophic moments estimation method which produces system of neutrosophic equations to derive the neutrosophic estimators using an algebraic isomorphism. Estimators based on two mentioned methods were derived successfully for some neutrosophic continuous probability distributions. Concept of neutrosophic Fisher information is also presented. Theorems were proved using an algebraic approach depending on the one-dimensional AH-Isometry. A simulation study is also presented to show the efficiency of the presented estimators.

Keywords

• ah isometry
• neutrosophic field of reals
• maximum likelihood
• neutrosophic fisher information